According to reports on the south coast, the Cherries have agreed a fee worth around £10m with the Blades for the ex-France Under-21 forward.
Mousset joined Bournemouth from Le Havre in 2016 for £5.7m and has made 71 appearances for the first team, mostly as a substitute.
The 23-year-old has scored five goals for the Cherries, netting in his only top-flight start of last season in a 5-1 loss at Arsenal in February.
The Blades have been linked with a number of striking targets, including Swansea City frontman Oli McBurnie and Brentford’s Neal Maupay.
United saw a £15m bid for Leeds-born McBurnie rejected earlier this week, but remain in the market to sign him.
Bradford City are entitled to a 15 per cent sell-on fee as part of any deal after selling the academy star to Swansea in 2015.
So far this summer, the Bramall Lane outfit have broken their transfer record twice to bring in Preston forward Callum Robinson and QPR midfielder Luke Freeman.
Doncaster Rovers have entered into talks to bring in a prospective assistant manager to work alongside Darren Moore and the appointment could be completed by the end of this week or the start of next week.
Moore’s preferred target is in work elsewhere, with Rovers aiming to secure his release.
Moore is keen to bring in a right-hand man following his appointment as Rovers boss.
The Rovers chief said: “They are in a little bit of a contractual situation but we are trying to find something out hopefully in the next couple of days.”
Hull City’s KCOM Stadium home is to stage its first England international in over a decade when England Under-21s host Kosovo in a Euro 2021 qualifer on September 9 (7.45pm).
The Tigers last hosted an under-21s game against Slovenia in August 2008.
Bradford City have appointed David Garth as the club’s new chief commercial officer.
As part of the club’s off-field restructure, Ryan Sparks has been appointed as director of communications. Garth began his career with the Bantams, before departing for Rangers in 2003.
He then went on to work for Manchester United and Inter Milan, prior to returning to the UK last year.